Electronic Correlations Control Interlayer Coupling and Magnetic Transition in MnBi$_2$Te$_4$/MnBr$_3$ Heterostructure

Huixia Fu; Jin Zhang; Xixi Yuan; Ying Zhao; Yuanhao Zhu; Zijing Ding

REVIEW 4 major objections 4 minor 46 references

Electronic Correlations Control Interlayer Coupling and Magnetic Transition in MnBi$_2$Te$_4$/MnBr$_3$ Heterostructure

T0 review · 4 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This paper claims that stacking a monolayer of MnBi2Te4 with one of MnBr3 raises the MnBi2Te4 layer's Curie temperature from about 13 K to 72 K, and that the Hubbard U on the MnBr3 layer decides whether the two layers order together or…

desk verdict New heterostructure, new mechanism, and a sane computational pipeline, but the headline Tc values are less solid than they look because the spin Hamiltonian used in Monte Carlo is never fully disclosed, and the key number is conditional on a single Hubbard U setting. read the letter →

arxiv 2506.13448 v1 pith:EQRZBJ4G submitted 2025-06-16 cond-mat.mtrl-sci physics.comp-ph

Yuanhao Zhu , Xixi Yuan , Ying Zhao , Jin Zhang , Zijing Ding , Huixia Fu This is my paper · ORCID

classification cond-mat.mtrl-sciphysics.comp-ph

keywords MnBi2Te4Br3vanderWaalsheterostructureCurietemperatureenhancementHubbardUinterlayermagneticcouplingphaseseparationMonteCarlosimulation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that a van der Waals stack of one monolayer of MnBi2Te4 and one monolayer of MnBr3 can raise the Curie temperature of the MnBi2Te4 layer from about 13 K to 72 K, a four- to fivefold increase. The control knob is the Hubbard U on the Mn-3d orbitals of MnBr3: at a moderate value (3.0 eV) the MnBr3 layer develops slight structural distortions that break its intralayer symmetry, strengthen the interlayer ferromagnetic exchange, and make the whole stack order in a single magnetic transition. At a stronger value (5.0 eV) the distortions disappear, the interlayer coupling weakens, and the two layers order separately at 56 K and 158 K. A sympathetic reader would care because the result points to a practical route for engineering higher-temperature two-dimensional magnets and suggests that magnetic transition behavior could be used to read off the strength of electronic correlations in a material.

What carries the argument

The argument is carried by a Heisenberg spin Hamiltonian fitted to density-functional energies through a machine-learning procedure and then simulated with Metropolis Monte Carlo on a $9 \times 9 \times 1$ supercell. Within that Hamiltonian the load-bearing quantity is the interlayer exchange $J_z^{B1}$, the dominant coupling between the Mn atoms of MnBr3 and the Mn atoms of ML-MBT; its sign and magnitude decide whether the stack shows one transition or two. The mechanism behind its variation is a seesaw between intralayer and interlayer exchange: as $U_2$ grows, the intralayer nearest-neighbor exchange $J_1^A$ strengthens while $J_z^{B1}$ weakens, and the structural asymmetry measured by Mn-Br bond-length and bond-angle differences and by the local-density-of-states splitting $\Delta_{\mathrm{dos}} = \mathrm{LDOS}(\text{central Mn}) - \mathrm{LDOS}(\text{nearest Mn})$ shrinks, vanishing near 3.8 eV. The Hamiltonian is built from Heisenberg exchange terms within each layer and across the interface, and the Monte Carlo simulation converts those fitted exchange constants into the reported transition temperatures.

What would settle it

Recompute the transition temperatures with the full spin Hamiltonian written out explicitly, including single-ion anisotropy and any other symmetry-breaking terms, and report the error of the machine-learning fit on the held-out 100 spin configurations; if the 72 K transition does not survive an anisotropy-corrected simulation, the enhancement claim is not settled. In parallel, a measured magnetization-versus-temperature curve of a grown stack that shows a single transition near 72 K would support the picture, while two separate transitions near 56 K and 158 K would match the decoupled $U_2 = 5.0$ eV case.

Watch

Extended reading notes

Core claim

The central discovery is that interfacing a monolayer of MnBi2Te4 (ML-MBT) with a monolayer of MnBr3 gives a ferromagnetically coupled stack in which ML-MBT orders at 72 K when the Hubbard $U_2$ on MnBr3 is 3.0 eV, compared with roughly 13 K for the isolated monolayer. The authors attribute the enhancement to $U_2$-dependent structural distortions in the MnBr3 layer: at 3.0 eV the two triangular regions of the MnBr3 supercell become inequivalent, producing a measurable asymmetry in Mn-Br bond lengths and bond angles, a splitting in the local density of states, and a strong interlayer exchange $J_z^{B1} = -6.91$ meV. Raising $U_2$ to 5.0 eV restores a nearly symmetric structure, drops that exchange to $-2.09$ meV, and drives the intralayer exchange $J_1^A$ from $-9.51$ to $-14.21$ meV; the result is two separate magnetic transitions at 56 K and 158 K, which the paper reads as the two layers decoupling. The same electron transfer from ML-MBT to MnBr3 is spin-polarized and weakens as $U_2$ grows, tying the charge redistribution to the magnetic coupling.

Load-bearing premise

The load-bearing assumption is that the Monte Carlo spin Hamiltonian the paper fits is complete enough to describe a two-dimensional magnet, including the magnetic anisotropy that allows order at finite temperature; the paper does not display those terms, and the quoted transition temperatures of 13, 72, 56, and 158 K would shift if the missing terms are wrong.

Editorial extensions

If this is right

Heterostructure assembly becomes a tunable lever: the same two materials can be made to order as one magnet at 72 K or as two magnets at 56 K and 158 K depending on the effective correlation strength in the MnBr3 layer.
A double-peaked heat capacity, rather than a single peak, becomes a fingerprint of interlayer decoupling and could be used in experiments to infer which $U$ regime a sample sits in.
The spin-polarized charge transfer from ML-MBT to MnBr3 means the interface simultaneously modifies the magnetic order and the electronic structure of the topological layer, so the stack is a candidate platform for proximity-tuned topological or spintronic devices.
The electron-counting rule that favors interlayer ferromagnetism at type-II/type-I interfaces suggests the design principle may transfer to other pairs of d-electron van der Waals monolayers, not only MnBi2Te4 and MnBr3.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper's own numbers imply a sharp crossover near $U_2 \approx 3.8$ eV where the LDOS splitting vanishes; a systematic scan of chemically substituted analogues with different effective $U$ could look for the predicted jump from one magnetic transition to two.
Because the mechanism works through structural distortion, biaxial strain on the MnBr3 layer could act as a substitute for tuning $U_2$: straining the layer toward the 3.0-eV geometry might reproduce the single-transition state even in a sample with stronger correlations.
The 72 K transition could also be read as proximity-induced ordering of the MBT layer by the high-$T_C$ MnBr3 rather than an intrinsic enhancement; a layer-resolved magnetization or element-specific measurement would separate the two readings.
If the anisotropy terms are as small as the paper's isotropic model implies, the transition temperatures should depend strongly on the simulation cell size; a finite-size scaling check would put a number on that sensitivity.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The paper's real novelty is the MBT/MnBr3 combination and the claim that the Hubbard U on the MnBr3 layer controls interlayer coupling through subtle structural distortions. The seesaw behavior between intralayer and interlayer exchange is a nice piece of physics, and the ML-MBT validation (Tc about 13 K) is a good benchmark. The electron-counting argument for FM interlayer coupling is consistent with prior literature. So there is genuine content here.

The soft spots are real but addressable. The biggest one: Equation (1) writes only isotropic Heisenberg terms, yet a strictly isotropic 2D Heisenberg model has no finite-Tc order. PASP must be fitting single-ion anisotropy or other symmetry-lowering terms somewhere, because the same pipeline gives 13 K for ML-MBT, but those terms are never shown, parameterized, or validated. The training/test behavior of the ML fit is also unreported. That means a reader cannot reproduce or fully trust the specific Tc numbers (72, 56, 158 K) from the text. This is the kind of omission a referee should catch and the authors can fix.

Second, the central prediction hangs on U2 = 3.0 eV. The authors are honest that 5.0 eV gives a different qualitative answer and even suggest using the transition as a probe of U, but that leaves the 72 K claim conditional. They need a stronger argument for why 3.0 eV is physical, or at least a systematic scan over reasonable U values with a discussion of which regime is likely.

Overall, this is a solid computational design study, not a finished result. The mechanism is plausible and the system is timely. I would send it to peer review and ask for the full Hamiltonian, ML test error, and a more robust U2 justification. The counting of isolated monolayers in the MC benchmark is also slightly crude but acceptable.

Referee Report

4 major / 4 minor

Summary. The manuscript proposes a van der Waals heterostructure consisting of monolayer MnBi2Te4 (ML-MBT) and monolayer MnBr3, and claims, on the basis of DFT+U calculations, machine-learned spin-Hamiltonian fitting (PASP), and Monte Carlo simulations, that the Curie temperature of the ML-MBT layer is enhanced by a factor of four to five, from about 13 K to 72 K, at a Hubbard U2 = 3.0 eV, with a single unified magnetic transition. At U2 = 5.0 eV the authors find that the layers magnetically decouple, producing two transitions at 56 K and 158 K. The proposed control mechanism is that the strength of U2 modifies structural distortions in MnBr3, which in turn set the interlayer ferromagnetic exchange interactions.

Significance. If the central prediction holds, the paper offers an interesting materials-design route: using electronic correlations in one layer to control interlayer magnetic coupling and the magnetic transition temperature of a topological-insulator monolayer. The computational pipeline is forward and non-circular: the Hubbard parameters are inputs, the Heisenberg exchanges are fitted to DFT energies, and the ML-MBT benchmark gives a TC of about 13 K, consistent with previous work. The claimed sensitivity of the result to U2 is honestly presented, and the authors explicitly note the difficulty of determining U2 from first principles. The main weaknesses are the incomplete disclosure of the spin Hamiltonian actually used in the Monte Carlo step and the lack of a quantitative justification for the specific U2 = 3.0 eV choice, both of which are load-bearing for the numerical TC values.

major comments (4)

[§III.B, Eq. (1)–(4)] The spin Hamiltonian written in the paper contains only bilinear isotropic Heisenberg exchange terms. As the authors themselves note in the Introduction, the Mermin-Wagner theorem forbids finite-temperature order in a two-dimensional isotropic Heisenberg model, so the finite Curie temperatures reported in Fig. 3 (13 K, 72 K, 56 K, 158 K) must arise from additional anisotropy or symmetry-breaking terms in the PASP Hamiltonian that are never written down, parameterized, or validated. Please provide the complete Hamiltonian actually used in the Monte Carlo simulations, including any single-ion anisotropy, Dzyaloshinskii-Moriya, or other spin invariants, together with their fitted values, and show how the quoted TCs depend on those terms. Without this, the numerical transition temperatures are not reproducible from the information given in the paper.
[§II, PASP fitting; §III.B, Fig. 2] The paper states that 500 random spin configurations were generated, with 400 used for training and 100 for testing, but no test error or fitting accuracy is reported anywhere. This is especially important because the central conclusion rests on the interlayer exchange couplings, which are small in magnitude compared with the intralayer couplings and are claimed to change substantially between U2 = 3.0 and 5.0 eV. Please report the root-mean-square error or a parity plot for the training and test sets, and specify the accuracy of the fitted interlayer couplings J_z. This is needed to establish that the machine-learned Hamiltonian faithfully reproduces the DFT energies, including for the configurations that determine the interlayer interactions.
[§III.B, Table I and Fig. 3; §IV] The central quantitative claim—the four- to fivefold enhancement of TC to 72 K and the single-transition behavior—is obtained only for U2 = 3.0 eV, while U2 = 5.0 eV gives a qualitatively different result (two transitions at 56 K and 158 K). The paper offers no independent determination of U2, such as constrained random-phase approximation or a fit to an experimental observable. Since the choice U2 = 3.0 eV is the linchpin of the main result, please either provide a first-principles or experimental justification for this value, or explicitly reframe the abstract and introduction so that the 72 K enhancement is presented as a conditional prediction of a parameter scan rather than as the paper's headline result. The summary does acknowledge the U2-dependence, but the framing in the Abstract and Introduction overstates the robustness of the 72 K value.
[§III.C, Fig. 5] The mechanism claim that structural distortions at U2 = 3.0 eV cause the enhanced interlayer coupling rests on the LDOS difference quantity Δdos, whose definition depends on the assignment of 'central' and 'nearest' Mn atoms in regions A and B. The paper does not state the numerical criteria used to define the two triangular regions or how many nearest neighbors are averaged. Please specify these definitions precisely, because the correlation between Δdos and J_z is central to the proposed seesaw mechanism and is otherwise not quantitatively assessable.

minor comments (4)

[§II, Methods] The convergence criterion 'total energy is less than 1×10⁻7 eV' should read '1×10⁻7 eV/atom' or equivalent, and the superscript formatting is corrupted in the manuscript text.
[Abstract and Introduction] The text contains a line break inside 'Néel temperature' ('Né el') and several other OCR-type artifacts (e.g., 'U1 = 5.0 eV is fixed' appears with missing characters in Fig. 2 caption area). Please proofread the final text.
[§III.B, Fig. 3] The black dashed curve is described as the 'numerical sum' of the isolated monolayer heat-capacity curves, but adding heat capacities does not yield the heat capacity of a non-interacting two-layer system unless the energy scales are comparable and the layer degrees of freedom are independent. As a schematic reference this is fine, but the wording should be softened to avoid implying a quantitatively rigorous decoupled limit.
[§III.B, Eq. (2)–(4)] The notation J_a^μ h_μ is not self-contained: the basis functions h_μ are deferred to the Supplemental Material, but the main text should at least state the order of the expansion and the number of independent parameters per shell, so that the reader can see how the 9+9+4+8+4+14 terms in Eqs. (2)–(4) are counted.

Circularity Check

0 steps flagged · score 0.0 of 10

The derivation is self-contained: Curie temperatures are forward Monte Carlo outputs from DFT-fitted exchange parameters, with no target quantity used to construct the model.

full rationale

The derivation chain is: DFT total energies for 500 random spin configurations, a machine-learning fit of Heisenberg exchange parameters from 400 training configurations (with 100 reserved for testing), and Monte Carlo simulation in which Curie temperatures are read off heat-capacity inflection points. No TC value enters the fitting procedure; the Hubbard parameters U1 and U2 are independently scanned physical inputs, and the exchange constants in Table I are outputs of the DFT+PASP fitting, not quantities chosen to reproduce the later TC values. The claimed 72 K, 56 K, and 158 K transitions are therefore forward predictions from the spin Hamiltonian. The initial ML-MBT validation (J1 = -1.387 meV, J2 = 0.089 meV, TC ~13 K) is checked against Ref. [47], an external published result, and is not used as a constraint on the heterostructure calculation. Self-citations appear only in background statements about other heterostructures (Refs. [33] and [34]) and are not load-bearing. The electron-counting rule [44] is an independent external rule used for qualitative consistency, and the DFT-computed negative interlayer exchanges independently confirm the FM interlayer coupling. The only substantive caveat is that Eq. (1) displays only isotropic Heisenberg exchange terms, so the finite-TC Monte Carlo results must implicitly rely on additional magnetic anisotropy or single-ion anisotropy terms that are not written or parameterized in the paper, and no ML fit test error is reported. That is a completeness, transparency, and correctness concern, not circularity, because the missing terms are not being reintroduced by using the computed TC as an input. No step in the paper reduces by construction to its own input.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The paper rests on a standard first-principles pipeline: DFT+U total energies, a machine-learned Heisenberg exchange fit, and Monte Carlo sampling. The main free inputs are the Hubbard parameters U1 and U2, especially U2, whose value changes the qualitative outcome (unified vs. split transition). The spin Hamiltonian is incompletely specified (anisotropy terms are absent from Eq. (1)), and the ML fit accuracy is unreported. No invented physical entities appear.

free parameters (5)

U2 (Hubbard U on Mn-3d in MnBr3) = 3.0 eV (sweep 3.0 to 5.0 eV in 0.2 eV steps)
The central prediction of a unified 72 K transition is obtained at U2 = 3.0 eV; at U2 = 5.0 eV the result changes qualitatively, so the value is load-bearing and not derived from experiment.
U1 (Hubbard U on Mn-3d in ML-MBT) = 5.0 eV
Fixed by hand in all heterostructure calculations; the authors report robustness to U1 but do not scan it for the main results.
Exchange interaction cutoff radius = 21 Bohr
Only spin pairs within 21 Bohr are included in the Heisenberg fit; no convergence test on this cutoff is reported.
Number of spin configurations for Hamiltonian fitting = 500 (400 train, 100 test)
The accuracy of the machine-learned Hamiltonian is not quantified with a test error or comparison to a validation set.
Monte Carlo supercell size and thermalization steps = 9x9x1 supercell; 1000 equilibration, 500 thermalization, 100 block steps
The extracted TC values depend on these simulation choices; no convergence checks with larger supercells or longer runs are shown.

assumptions (5)

domain assumption PBE+U with the Dudarev correction and DFT-D3 dispersion describes the electronic structure and magnetic interactions of the MBT/MnBr3 interface adequately.
Used in all calculations (Section II); the U choice itself is an input, and the functional is an approximation for strongly correlated 3d systems.
domain assumption Magnetic interactions are fully captured by a bilinear Heisenberg Hamiltonian plus unspecified anisotropy terms that stabilize finite-temperature order.
Eq. (1) displays only exchange terms, and the method text mentions spin invariants; the full Hamiltonian, including the terms needed for a finite TC in 2D, is not shown.
domain assumption The machine-learning fit using 500 configurations is accurate enough to predict exchange parameters and transition temperatures.
The test set is mentioned but no error metric is given; the fit is a black-box step in the pipeline.
ad hoc to paper The C3-symmetric stacking is the relevant experimental interface.
Section III.A states the configuration was chosen to preserve C3 symmetry and reduce computational cost; sliding and spacing stability are checked, but other registries are not.
domain assumption The electron-counting rule of Ref. [44] correctly predicts interlayer FM coupling for this interface.
Used in Section III.A as a consistency argument; it is not the basis of the quantitative results.

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Cite this review

Pith. "Pith review of Electronic Correlations Control Interlayer Coupling and Magnetic Transition in MnBi$_2$Te$_4$/MnBr$_3$ Heterostructure." pith.science (2026). https://pith.science/paper/EQRZBJ4G

@misc{pith2026250613448,
  author       = {Pith},
  title        = {Pith review of: Electronic Correlations Control Interlayer Coupling and Magnetic Transition in MnBi$_2$Te$_4$/MnBr$_3$ Heterostructure},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EQRZBJ4G}},
  note         = {Machine review of arXiv:2506.13448}
}

abstract

Bulk MnBi$_2$Te$_4$ (MBT) is an intrinsic antiferromagnetic topological insulator. However, its low N\'eel temperature of $\sim 25\,\mathrm{K}$ severely restricts its practical applications. Here, we propose a van der Waals heterostructure composed of monolayer MBT (ML-MBT) and monolayer MnBr$_3$, an intrinsic Chern insulator possessing a high Curie temperature ($T_\mathrm{C} \sim 200\,\mathrm{K}$). By employing density functional theory calculations and Monte Carlo simulations, we demonstrate that interfacing ML-MBT with MnBr$_3$ significantly enhances the $T_\mathrm{C}$ of ML-MBT by a factor of four to five. Electronic correlations characterized by the Hubbard parameter $U_2$ for Mn-$d$ orbitals in MnBr$_3$ play a crucial role in governing magnetic coupling within the system. At a moderate correlation strength of $U_2 = 3.0\,\mathrm{eV}$, slight structural distortions in MnBr$_3$ break intralayer symmetry, enabling robust interlayer ferromagnetic coupling and yielding a single, unified magnetic transition. Increasing $U_2$ reduces these structural distortions, weakens interlayer coupling, and induces two distinct magnetic transitions, indicating interlayer magnetic decoupling. Thus, the MBT/MnBr$_3$ heterostructure offers a novel approach for controlling magnetic order and enhancing the performance of spintronic devices.

Figures

Figures reproduced from arXiv: 2506.13448 by the authors.

**Figure 2.** FIG 2. (a) [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG 3. Temperature [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: FIG 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: FIG 5. Enlarged LDOS plots for region [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

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Works this paper leans on

46 extracted references · 41 canonical work pages

[1]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81, 109 (2009)

2009
[2]

J. R. Schaibley, H. Yu, G. Clark, P. Rivera, J. S. Ross, K. L. Seyler, W. Yao, and X. Xu, Valleytronics in 2D materials, Nat. Rev. Mater. 1, 16055 (2016)

2016
[3]

Chhowalla, D

M. Chhowalla, D. Jena, and H. Zhang, Two-dimensional semiconductors for transistors, Nat. Rev. Mater. 1, 16052 (2016)

2016
[4]

Manzeli, D

S. Manzeli, D. Ovchinnikov, D. Pasquier, O. V. Yazyev, and A. Kis, 2D transition metal dichalcogenides, Nat. Rev. Mater. 2, 17033 (2017)

2017
[5]

Huang, G

B. Huang, G. Clark, E. Navarro-Moratalla et al., Layer- dependent ferromagnetism in a van der Waals crystal down to the monolayer limit, Nature 546, 270 (2017)

work page 2017
[6]

Z. Sun, Y. Yi, T. Song et al., Giant nonreciprocal second- harmonic generation from antiferromagnetic bilayer CrI3, Nature 572, 497 (2019)

work page 2019
[7]

C, Gong , L. Li , Z . Li et al. Discovery of intrinsic ferromagnetism in two -dimensional van der Waals crystals, Nature 546, 265 (2017)

work page 2017
[8]

G. T. Lin, H. L. Zhuang , X. Luo , B. J. Liu et al. , Tricritical behavior of the two -dimensional intrinsically ferromagnetic semiconductor CrGeTe3, Phys. Rev. B 95, 245212 (2017)

work page 2017

Show all 46 references

[9]

C. Gong, X. Zhang, Two-dimensional magnetic crystals and emergent heterostructure devices , Science 363, eaav4450 (2019)

2019
[10]

Burch, D

K. Burch, D . Mandrus, J . Park, Magnetism in two - dimensional van der Waals materials , Nature 563, 47 (2018)

2018
[11]

Q. Wang, A. Bedoya-Pinto, M. Blei et al., The magnetic genome of two -dimensional van der Waals materials , ACS nano 16, 6960 (2022)

2022
[12]

Z. Fei, B. Huang, P. Malinowski, W. Wang, T. Song, J. Sanchez, W. Yao, D. Xiao, X. Zhu, A. F. May, W. Wu, D. H. Cobden, J.-H. Chu, and X. Xu, Magnetism in two- dimensional van der Waals materials, Nat. Mater. 17, 778 (2018)

2018
[13]

X. Wang, K. Du, Y. Y. F. Liu et al., Raman spectroscopy of atomically thin two -dimensional magnetic iron phosphorus trisulfide (FePS 3) crystals , 2D Mater. 3, 031009 (2016)

2016
[14]

J.-U. Lee, S. Lee, J. H. Ryoo, S. Kang, T. Y. Kim, P. Kim, C.-H. Park, J. -G. Park, and H. Cheong, Ising -Type Magnetic Ordering in Atomically Thin FePS3, Nano Lett. 16, 7433 (2016)

2016
[15]

Bonilla, S

M. Bonilla, S. Kolekar, Y. Ma, H. C. Diaz et al., Strong room-temperature ferromagnetism in VSe 2 monolayers on van der Waals substrates , Nature Nanotech. 13, 289 (2018)

2018
[16]

N. D. Mermin and H. Wagner, Absence of Ferromagnetism or Antiferromagnetism in One- or Two- Dimensional Isotropic Heisenberg Models, Phys. Rev. Lett. 17, 1133 (1966)

1966
[17]

X. Li, B. Dong, X. Sun, H. Wang, T. Yang, G. Yu, and Z. V. Han, Perspectives on exfoliated two -dimensional spintronics, J. Semicond. 40, 081508 (2019)

2019
[18]

J.-Y. You, Z. Zhang, X.-J. Dong, B. Gu, and G. Su, Two- dimensional magnetic semiconductors with room Curie temperatures, Phys. Rev. Research 2, 013002 (2020)

2020
[19]

Jiang, J

S. Jiang, J. Shan, and K. F. Mak, Electric-field switching of two-dimensional van der Waals magnets, Nat. Mater. 17, 406 (2018)

2018
[20]

J.-Y. You, Z. Zhang, B. Gu, and G. Su, Two-Dimensional Room-Temperature Ferromagnetic Semiconductors with Quantum Anomalous Hall Effect, Phys. Rev. Appl. 12, 024063 (2019)

2019
[21]

et al., Large magnetic gap at the Dirac point in Bi2Te3/MnBi2Te4 heterostructures

Rienks, E.D.L., Wimmer, S., Sá nchez-Barriga, J. et al., Large magnetic gap at the Dirac point in Bi2Te3/MnBi2Te4 heterostructures. Nature 576, 423 (2019)

2019
[22]

M. M. Otrokov, I. I. Klimovskikh, H. Bentmann, D. Estyunin, A. Zeugner et al. Prediction and observation of an antiferromagnetic topological insulator , Nature 576, 416 (2019)

2019
[23]

Otrokov, I

M. Otrokov, I. P u ov, M. Blanco -Rey, M. Hoffmann, Yu. Vyazovskaya, S V. Eremeev, A. Ernst, P. he que, A. Arnau et al . Unique thickness-dependent properties of the van der Waals interlayer antiferromagnet MnBi 2Te4 films, Phys. Rev. Lett. 122, 107202 (2019)

2019
[25]

J. You, X. Dong, B. Gu, and G. Su, Electric field induced topological phase transition and large enhancements of spin-orbit coupling and Curie temperature in two - dimensional ferromagnetic semiconductors, Phys. Rev. B 103, 104403 (2021)

2021
[26]

Y. Liu, Y. Huang, and X. Duan, Van der Waals integration before and beyond two-dimensional materials, Nature (London) 567, 323 (2019)

2019
[27]

Gibertini, M

M. Gibertini, M. Koperski, A. F. Morpurgo, and K. S. Novoselov, Magnetic 2D materials and heterostructures, Nat. Nanotechnol. 14, 408 (2019)

2019
[28]

C. Jin, E. Y. Ma, O. Karni, E. C. Regan, F. Wang, and T. F. Heinz, Ultrafast dynamics in van der Waals heterostructures, Nat. Nanotechnol. 13, 994 (2018)

2018
[29]

K. S. Novoselov, A. Mishchenko, A. Carvalho, and A. H. C. Neto, 2D materials and van der Waals heterostructures, Science 353, 9439 (2016)

2016
[30]

Liu and M

X. Liu and M. C. Hersam, Interface characterization and control of 2D materials and heterostructures, Adv. Mater. 30, 1801586 (2018)

2018
[31]

M.-Y. Li, C. -H. Chen, Y. Shi, and L. -J. Li, Heterostructures based on two -dimensional layered materials and their potential applications, Mater. Today (Oxford, U. K.) 19, 322 (2016)

2016
[32]

F. Xue, Z. Wang, Y. Hou, L. Gu, and R. Wu, Control of magnetic properties of MnBi 2Te4 using a van der Waals ferroelectric III2− I3 film and biaxial strain, Phys. Rev. B 101, 184426 (2020)

2020
[33]

H. Fu, C. Liu, and B. Yan, Exchange bias and quantum anomalous Hall effect in the MnBi 2Te4/CrI3 heterostructure, Science Advances 6, eaaz0948 (2020)

2020
[34]

R. Yang, X. Man, J. Peng, J. Zhang, F. Wang, F. Wang, H. Zhang, and X. Xu, Septuple XBi2Te4 (X = Ge, Sn, Pb) intercalated MnBi 2Te4 for realizing interlayer ferromagnetism and quantum anomalous hall effect , npj Quantum Mater. 10, 3 (2025)

2025
[35]

F. Xie, Z. Yin, B. Zhou and Y. Ding, Tunable electronic band structure and magnetic anisotropy in two - dimensional Dirac half-metal MnBr3 by external stimulus: strain, magnetization direction, and interlayer coupling , Phys. Chem. Chem. Phys. 25, 32515 (2023)

2023
[36]

Kresse, and J

G. Kresse, and J. Furthmü ller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996)

1996
[37]

P. E. Blö chl, Projector augmented-wave method , Phys. Rev. B 50, 17953 (1994)

1994
[38]

J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett . 77, 3865 (1996)

1996
[39]

S. L. Dudarev , G. A. Botton , S. Y. Savrasov , C. J. Humphreys, and A. P. Sutton , Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+ U study, Phys. Rev. B 57, 1505 (1998)

1998
[40]

Grimme, J

S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu, J. Chem. Phys. 132, 154104 (20100)
[41]

F. Lou, X. Li, J. Ji, H. Yu, J. Feng, X. Gong, and H. Xiang, PASP: Property analysis and simulation package for materials, J. Chem. Phys. 154, 114103 (2021)

2021
[42]

Q. Sun, N. Kioussis, Prediction of manganese trihalides as two-dimensional Dirac half -metals, Phys. Rev. B 97, 094408 (2018)

2018
[43]

Y. Li, Z. Jiang, J. Li, S. Xu, and W. Duan, Magnetic anisotropy of the two -dimensional ferromagnetic insulator MnBi2Te4, Phys. Rev. B 100, 134438 (2019)

2019
[44]

Xiao, and B

J. Xiao, and B. Yan, An electron -counting rule to determine the interlayer magnetic coupling of the van der Waals materials, 2D Mater. 7, 045010 (2020)

2020
[45]

Figueroa, F

I. Figueroa, F. Bonell, G. Cuxart et al. , Absence of magnetic proximity effect at the interface of Bi2Se3 and (Bi,Sb)2Te3 with EuS , Phys. Rev. Lett. 125, 226801 (2020)

2020
[46]

C. Yang, L. Pan, A. J. Grutter et al. , Termination switching of antiferromagnetic proximity effect in topological insulator , Science Advances 6, eaaz8463 (2020)

2020
[47]

Zhao , L

Y. Zhao , L . Zhou , F . Wang et al. , Even–odd layer - dependent anomalous Hall effect in topological magnet MnBi2Te4 thin films. Nano lett. 21, 7691 (2021)

2021

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81, 109 (2009)

2009

[2] [2]

J. R. Schaibley, H. Yu, G. Clark, P. Rivera, J. S. Ross, K. L. Seyler, W. Yao, and X. Xu, Valleytronics in 2D materials, Nat. Rev. Mater. 1, 16055 (2016)

2016

[3] [3]

Chhowalla, D

M. Chhowalla, D. Jena, and H. Zhang, Two-dimensional semiconductors for transistors, Nat. Rev. Mater. 1, 16052 (2016)

2016

[4] [4]

Manzeli, D

S. Manzeli, D. Ovchinnikov, D. Pasquier, O. V. Yazyev, and A. Kis, 2D transition metal dichalcogenides, Nat. Rev. Mater. 2, 17033 (2017)

2017

[5] [5]

Huang, G

B. Huang, G. Clark, E. Navarro-Moratalla et al., Layer- dependent ferromagnetism in a van der Waals crystal down to the monolayer limit, Nature 546, 270 (2017)

work page 2017

[6] [6]

Z. Sun, Y. Yi, T. Song et al., Giant nonreciprocal second- harmonic generation from antiferromagnetic bilayer CrI3, Nature 572, 497 (2019)

work page 2019

[7] [7]

C, Gong , L. Li , Z . Li et al. Discovery of intrinsic ferromagnetism in two -dimensional van der Waals crystals, Nature 546, 265 (2017)

work page 2017

[8] [8]

G. T. Lin, H. L. Zhuang , X. Luo , B. J. Liu et al. , Tricritical behavior of the two -dimensional intrinsically ferromagnetic semiconductor CrGeTe3, Phys. Rev. B 95, 245212 (2017)

work page 2017